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Chapter 34: Problem 2

When two light waves, both with wavelength \(\lambda\) and amplitude \(A\), interfere constructively, they produce a light wave of the same wavelength but with amplitude \(2 A .\) What will be the intensity of this light wave? a) same intensity as before b) double the intensity c) quadruple the intensity d) not enough information

Short Answer

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Question: When two light waves of the same wavelength and amplitude interfere constructively, the intensity of the resulting wave is: a) Half the intensity b) Double the intensity c) Quadruple the intensity d) Equal to the intensity Answer: c) Quadruple the intensity

Step by step solution

01

Constructive interference of two waves

When two light waves of the same wavelength and amplitude interfere constructively, their amplitudes add up, which results in a wave with the same wavelength but twice the amplitude. So the amplitude of the resulting wave will be \(2 A\).
02

Relation between amplitude and intensity

The intensity of a wave is proportional to the square of its amplitude. Mathematically, this can be expressed as: \(I \propto A^2\) where \(I\) is the intensity and \(A\) is the amplitude of the wave.
03

Find the intensity of the resulting wave

As per the relationship, the intensity of the resulting wave will be proportional to the square of its amplitude \((2A)^2\). \(I_{result} \propto (2A)^2 = 4A^2\)
04

Compare the intensity of the resulting wave with the initial intensity

Since the intensity of the original waves is proportional to \(A^2\), let's compare the resulting intensity with the initial intensity: \(\frac{I_{result}}{I_{initial}} = \frac{4A^2}{A^2} = 4\)
05

Choose the correct option

The intensity of the resulting wave is 4 times the intensity of the original waves. So, the correct answer is option c) Quadruple the intensity.

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